Challenge yourself! – Grades 9-10 (Polynomial Expansion)

How many distinct terms does $(x+y+z)^{15}$ have in its expanded form?

As an example, $(x+y+z)^2$ has $6$ terms in its expanded form since $(x+y+z)^2 = x^2+y^2+z^2+2xy+2yz+2xz$ .

Note that we are not interested in finding the expansion of $(x+y+z)^{15}$ . We are interested in just the number of distinct terms in the expansion!

Hint: Think about the degree of each term in the expansion.